I recently had a similar problem running AE CS4 9.0.2 on a Mac running OS X 10.5.7.
What I discovered was that three files in my Library/QuickTime folder were crashing AE on start up. These files were:
Flip4Mac WMV Advanced.component
Flip4Mac WMV Export.component
Flip4Mac WMV Import.component
After I discovered this, I went to the Flip4Mac website (https://www.telestream.net/flip4mac-wmv/overview.htm) and downloaded the latest free version of the program. After I installed that, AE started up fine.
Hope this helps!